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32.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91
33.\" $Id: erf.3,v 1.4 2004/12/20 21:35:45 scp Exp $
34.\"
35.Dd December 11, 2006
36.Dt ERF 3
37.Os BSD 4.3
38.Sh NAME
39.Nm erf ,
40.Nm erfc
41.Nd error function operators
42.Sh SYNOPSIS
43.Fd #include <math.h>
44.Ft double
45.Fn erf "double x"
46.Ft long double
47.Fn erfl "long double x"
48.Ft float
49.Fn erff "float x"
50.Ft double
51.Fn erfc "double x"
52.Ft long double
53.Fn erfcl "long double x"
54.Ft float
55.Fn erfcf "float x"
56.Sh DESCRIPTION
57These functions calculate the error function of
58.Fa x .
59.Pp
60The
61.Fn erf
62function calculates the error function of x; where
63.Bd -filled -offset indent
64.if n \{\
65erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \}
66.if t \{\
67erf\|(x) :=
68(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \}
69.Ed
70.Pp
71The
72.Fn erfc
73function calculates the complementary error function of
74.Fa x ;
75that is
76.Fn erfc
77computes the difference of the error function
78.Fn erf x
79from 1.0.
80This is useful, since for large
81.Fa x
82use of
83.Fn erfc
84avoids loss of precision due to cancellation.
85.Sh SPECIAL VALUES
86.Fn erf "�0"
87returns �0.
88.Pp
89.Fn erf "�infinity"
90returns �1.
91.Pp
92.Fn erfc "-infinity"
93returns 2.
94.Pp
95.Fn erfc "+infinity"
96returns +0.
97.Sh SEE ALSO
98.Xr math 3
99.Sh STANDARDS
100The
101.Fn erf
102and
103.Fn erfc
104functions conform to ISO/IEC 9899:1999(E).